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Stereo Image Coder Based on the MRF Model for Disparity Compensation


This paper presents a stereoscopic image coder based on the MRF model and MAP estimation of the disparity field. The MRF model minimizes the noise of disparity compensation, because it takes into account the residual energy, smoothness constraints on the disparity field, and the occlusion field. Disparity compensation is formulated as an MAP-MRF problem in the spatial domain, where the MRF field consists of the disparity vector and occlusion fields. The occlusion field is partitioned into three regions by an initial double-threshold setting. The MAP search is conducted in a block-based sense on one or two of the three regions, providing faster execution. The reference and residual images are decomposed by a discrete wavelet transform and the transform coefficients are encoded by employing the morphological representation of wavelet coefficients algorithm. As a result of the morphological encoding, the reference and residual images together with the disparity vector field are transmitted in partitions, lowering total entropy. The experimental evaluation of the proposed scheme on synthetic and real images shows beneficial performance over other stereoscopic coders in the literature.


  1. 1.

    Yamaguchi H, Tatehira Y, Akiyama K, Kobayashi Y: Stereoscopic images disparity for predictive coding. Proceedings of IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP '89), May 1989, Glasgow, Scotland, UK 3: 1976–1979.

    Google Scholar 

  2. 2.

    Lucas BD, Kanade T: An iterative image registration technique with an application to stereo vision. Proceedings of 7th International Joint Conference on Artificial Intelligence (IJCAI '81), August 1981, Vancouver, BC, Canada 674–679.

    Google Scholar 

  3. 3.

    Woo W, Ortega A: Overlapped block disparity compensation with adaptive windows for stereo image coding. IEEE Transactions on Circuits and Systems for Video Technology 2000, 10(2):194–200. 10.1109/76.825718

    Article  Google Scholar 

  4. 4.

    Jiang J, Edirisinghe EA: A hybrid scheme for low bit-rate coding of stereo images. IEEE Transactions on Image Processing 2002, 11(2):123–134. 10.1109/83.982820

    Article  Google Scholar 

  5. 5.

    Sethuraman S, Jordan A, Siegel M: Multiresolution based hierarchical disparity estimation for stereo image pair compression. Proceedings of Symposium on Applications of Subbands and Wavelets, March 1994, Newark, NJ, USA

    Google Scholar 

  6. 6.

    Woo W, Ortega A: Stereo image compression with disparity compensation using the MRF model. Visual Communications and Image Processing (VCIP '96), March 1996, Orlando, Fla, USA, Proceedings of SPIE 2727: 28–41.

    Article  Google Scholar 

  7. 7.

    Yamaguchi H, Tatehira Y, Akiyama K, Kobayashi Y: Data compression and depth shape reproduction of stereoscopic images. Systems and Computers in Japan 1991, 22(12):53–64. 10.1002/scj.4690221205

    Article  Google Scholar 

  8. 8.

    Boulgouris NV, Strintzis MG: A family of wavelet-based stereo image coders. IEEE Transactions on Circuits and Systems for Video Technology 2002, 12(10):898–903. 10.1109/TCSVT.2002.804895

    Article  Google Scholar 

  9. 9.

    Frajka T, Zeger K: Residual image coding for stereo image compression. Optical Engineering 2003, 42(1):182–189. 10.1117/1.1526492

    Article  Google Scholar 

  10. 10.

    Ellinas JN, Sangriotis MS: Stereo image compression using wavelet coefficients morphology. Image and Vision Computing 2004, 22(4):281–290. 10.1016/j.imavis.2003.09.017

    Article  Google Scholar 

  11. 11.

    Perkins MG: Data compression of stereopairs. IEEE Transactions on Communications 1992, 40(4):684–696. 10.1109/26.141424

    Article  Google Scholar 

  12. 12.

    Aydinoglu H, Hayes MH: Stereo image coding: a projection approach. IEEE Transactions on Image Processing 1998, 7(4):506–516. 10.1109/83.663495

    Article  Google Scholar 

  13. 13.

    Geman S, Geman D: Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 1984, 6(6):721–741.

    Article  Google Scholar 

  14. 14.

    Konrad J, Dubois E: Bayesian estimation of motion vector fields. IEEE Transactions on Pattern Analysis and Machine Intelligence 1992, 14(9):910–927. 10.1109/34.161350

    Article  Google Scholar 

  15. 15.

    Zhang J, Hanauer GG: The application of mean field theory to image motion estimation. IEEE Transactions on Image Processing 1995, 4(1):19–33. 10.1109/83.350816

    Article  Google Scholar 

  16. 16.

    Wei J, Li Z-N: An efficient two-pass MAP-MRF algorithm for motion estimation based on mean field theory. IEEE Transactions on Circuits and Systems for Video Technology 1999, 9(6):960–972. 10.1109/76.785734

    Article  Google Scholar 

  17. 17.

    Ellinas JN, Sangriotis MS: Stereo image coder based on MRF analysis for disparity estimation and morphological encoding. Proceedings of 2nd IEEE International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT '04), September 2004, Thessaloniki, Greece 852–859.

    Google Scholar 

  18. 18.

    Servetto SD, Ramchandran K, Orchard MT: Image coding based on a morphological representation of wavelet data. IEEE Transactions on Image Processing 1999, 8(9):1161–1174. 10.1109/83.784429

    Article  Google Scholar 

  19. 19.

    Lukacs M: Predictive coding of multi-view point image sets. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '86), April 1986, Tokyo, Japan 11: 521–524.

    Article  Google Scholar 

  20. 20.

    Starck J-L, Murtagh FD, Bijaoui A: Image Processing and Data Analysis: The Multiscale Approach. Cambridge University Press, Cambridge, UK; 1998.

    Google Scholar 

  21. 21.

    Li SZ: Markov Random Field Modeling in Computer Vision. Springer, Tokyo, Japan; 1995.

    Google Scholar 

  22. 22.

    Li SZ: Markov random field models in computer vision. Proceedings of 3rd European Conference on Computer Vision (ECCV '94), May 1994, Stockholm, Sweden 2: 361–370.

    Google Scholar 

  23. 23.

    Besag J: Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society B 1974, 36: 192–225.

    MathSciNet  MATH  Google Scholar 

  24. 24.

    Antonini M, Barlaud M, Mathieu P, Daubechies I: Image coding using wavelet transform. IEEE Transactions on Image Processing 1992, 1(2):205–220. 10.1109/83.136597

    Article  Google Scholar 

  25. 25.

    Shapiro JM: Embedded image coding using zero trees of wavelet coefficients. IEEE Transactions on Signal Processing 1993, 41(12):3445–3462. 10.1109/78.258085

    Article  Google Scholar 

  26. 26.

    Said A, Pearlman WA: A new, fast, and efficient image codec based on set partitioning in hierarchical trees. IEEE Transactions on Circuits and Systems for Video Technology 1996, 6(3):243–250. 10.1109/76.499834

    Article  Google Scholar 

  27. 27.

    Chai B-B, Vass J, Zhuang X: Significance-linked connected component analysis for wavelet image coding. IEEE Transactions on Image Processing 1999, 8(6):774–784. 10.1109/83.766856

    Article  Google Scholar 

  28. 28.

    Dubois E, Konrad J: Estimation of 2-D motion fields from image sequences with application to motion-compensated processing. In Motion Analysis and Image Sequence Processing. Edited by: Sezan MI, Lagendijk RL. Kluwer Academic, Boston, Mass, USA; 1993:53–87.

    Google Scholar 

  29. 29.

    Stereo images from Bonn University, available from:

  30. 30.

    Stereo images from Carnegie Mellon University, Pittsburgh, Pa, USA, available from:

  31. 31.

  32. 32.

    Usevitch BE: A tutorial on modern lossy wavelet image compression: foundations of JPEG 2000. IEEE Signal Processing Magazine 2001, 18(5):22–35. 10.1109/79.952803

    Article  Google Scholar 

  33. 33.

    Adams MD, Man H, Kossentini F, Ebrahimi T: JPEG 2000: The next generation still image compression standard. ISO/IEC JTC 1/SC 29/WG 1 N 1734, 2000

    Google Scholar 

  34. 34.

    Woo W, Ortega A: Optimal blockwise dependent quantization for stereo image coding. IEEE Transactions on Circuits and Systems for Video Technology 1999, 9(6):861–867. 10.1109/76.785724

    Article  Google Scholar 

  35. 35.

    Woo W, Ortega A, Iwadate Y: Stereo image coding using hierarchical MRF model and selective overlapped block disparity compensation. Proceedings of IEEE International Conference on Image Processing (ICIP '99), October 1999, Kobe, Japan 2: 467–471.

    Article  Google Scholar 

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Ellinas, J.N., Sangriotis, M.S. Stereo Image Coder Based on the MRF Model for Disparity Compensation. EURASIP J. Adv. Signal Process. 2006, 073950 (2006).

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  • Wavelet Coefficient
  • Residual Energy
  • Stereo Image
  • Total Entropy
  • Image Coder